Well when we're talking about search - both the Yahoo and Live engines have effectively caught up in providing relevant results when searching, yet Google still has a dominating position which is still growing.
That right there is a result of branding.
It's the same reason why Coke dominates the soda market, if someone walks into a store to get a drink of some form, the chance that they will get a Coke is high - when any of the drinks will essentially do the same job.
To add some perspective I'll give a recent personal experience, which isn't conclusive by any stretch but illustrates my point easily enough.
I have an Uncle who approached me last week asking for advice about buying his first computer because he wanted to get onto the Internet so that he could search for Surfing stuff (his hobby) and also use Ebay. He's never used the net before, but already has a good idea of what Ebay is, and can name sites like Google (but not yahoo interestingly enough).
